Approximation of Continuous Functions by de La Vallee-Poussin Operators

Abstract

For $\sigma \rightarrow \infty$, we study the asymptotic behavior of upper bounds of deviations of functions blonding to the classes $\widehat{C}_{\infty}^{\overline{\Psi}}$ and $\widehat{C}^{\overline{\Psi}} H_{\omega}$ from the so-called Vallee Poussin operators. We find asymptotic equalities that, in some important cases, guarantee the solution of the Kolmogorov - Nikol's'kyi problem for the Vallee Poussin operators on the classes $\widehat{C}_{\infty}^{\overline{\Psi}}$ and $\widehat{C}^{\overline{\Psi}} H_{\omega}$.